Characterizations of Bounded Singular Integral Operators on the Fock Space and Their Berezin Transforms
Year: 2023
Author: Xingtang Dong, Li Feng
Analysis in Theory and Applications, Vol. 39 (2023), Iss. 2 : pp. 105–119
Abstract
There is a singular integral operators $S_{\varphi}$ on the Fock space $\mathcal{F}^2(\mathbb{C}),$ which originated from the unitarily equivalent version of the Hilbert transform on $L^2(\mathbb{R}).$ In this paper, we give an analytic characterization of functions $\varphi$ with finite zeros such that the integral operator $S_{\varphi}$ is bounded on $\mathcal{F}^2(\mathbb{C})$ using Hadamard’s factorization theorem. As an application, we obtain a complete characterization for such symbol functions $\varphi$ such that the Berezin transform of $S_{\varphi}$ is bounded while the operator $S_{\varphi}$ is not. Also, the corresponding problem in higher dimensions is considered.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2021-0034
Analysis in Theory and Applications, Vol. 39 (2023), Iss. 2 : pp. 105–119
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Fock space singular integral operators boundedness Berezin transform.